Subgroups - Solved Example

Post Reply
User avatar
Eli
Senior Expert Member
Reactions: 183
Posts: 5303
Joined: 9 years ago
Location: Tanzania
Has thanked: 75 times
Been thanked: 88 times
Contact:
Contact Eli

#1

is a subgroup of a group if the identity element belongs to ; and also the inverse element belongs to . We illustrate this by example.

Example 1

If is an abelian group and if show that is a subgroup of .

Solution

(i) hence

(ii) If then so

(iii) If that's , multiplying both sides of the equality by we get



Hence and thus is a subgroup of
0
TSSFL -- A Creative Journey Towards Infinite Possibilities!
Top
Post Reply

Return to “Abstract Algebra”

  • Information

  • Who is online

    Users browsing this forum: No registered users and 0 guests